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 A364230 Triangle read by rows: T(n, k) is the number of n X n symmetric Toeplitz matrices of rank k using all the integers 1, 2, ..., n. 1
 1, 0, 2, 0, 0, 6, 0, 0, 0, 24, 0, 0, 0, 0, 120, 0, 0, 0, 0, 2, 718, 0, 0, 0, 0, 4, 31, 5005, 0, 0, 0, 0, 0, 2, 44, 40274, 0, 0, 0, 0, 0, 0, 4, 272, 362604, 0, 0, 0, 0, 0, 0, 0, 111, 774, 3627915, 0, 0, 0, 0, 0, 0, 2, 14, 244, 6974, 39909566, 0, 0, 0, 0, 0, 0, 0, 4, 64, 743, 9533, 478991256 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..78. Wikipedia, Toeplitz Matrix EXAMPLE The triangle begins: 1; 0, 2; 0, 0, 6; 0, 0, 0, 24; 0, 0, 0, 0, 120; 0, 0, 0, 0, 2, 718; 0, 0, 0, 0, 4, 31, 5005; ... MATHEMATICA T[n_, k_]:= Count[Table[MatrixRank[ToeplitzMatrix[Part[Permutations[Range[n]], i]]], {i, n!}], k]; Table[T[n, k], {n, 8}, {k, n}]//Flatten PROG (PARI) MkMat(v)={matrix(#v, #v, i, j, v[1+abs(i-j)])} row(n)={my(f=vector(n)); forperm(vector(n, i, i), v, f[matrank(MkMat(v))]++); f} \\ Andrew Howroyd, Dec 30 2023 CROSSREFS Cf. A000142 (row sums), A350953 (minimal determinant), A350954 (maximal determinant), A351019 (minimal permanent), A351020 (maximal permanent), A356865 (minimal nonzero absolute value determinant), A364231 (right diagonal). Sequence in context: A106512 A181229 A364233 * A259857 A364790 A094785 Adjacent sequences: A364227 A364228 A364229 * A364231 A364232 A364233 KEYWORD nonn,tabl AUTHOR Stefano Spezia, Jul 14 2023 EXTENSIONS Terms a(46) and beyond from Andrew Howroyd, Dec 30 2023 STATUS approved

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Last modified July 14 20:49 EDT 2024. Contains 374323 sequences. (Running on oeis4.)